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Rashid [163]
3 years ago
15

HELP me fill in the correct things in the guest a check list.

Mathematics
1 answer:
photoshop1234 [79]3 years ago
5 0
6 pairs of shoes and 40 hats
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Find integra of xlnxdx
Mademuasel [1]

Answer:

\dfrac{1}{2}x^2\ln x - \dfrac{1}{4}x^2+\text{C}

Step-by-step explanation:

<u>Fundamental Theorem of Calculus</u>

\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))

If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a <u>constant of integration</u>.

\boxed{\begin{minipage}{4 cm}\underline{Integrating $x^n$}\\\\$\displaystyle \int x^n\:\text{d}x=\dfrac{x^{n+1}}{n+1}+\text{C}$\end{minipage}}

Increase the power by 1, then divide by the new power.

Given <u>indefinite integral</u>:

\displaystyle \int x \ln x \:\: \text{d}x

To integrate the given integral, use Integration by Parts:

\boxed{\begin{minipage}{5 cm}\underline{Integration by parts} \\\\$\displaystyle \int u \dfrac{\text{d}v}{\text{d}x}\:\text{d}x=uv-\int v\: \dfrac{\text{d}u}{\text{d}x}\:\text{d}x$ \\ \end{minipage}}

\text{Let }u=\ln x \implies \dfrac{\text{d}u}{\text{d}x}=\dfrac{1}{x}

\text{Let }\dfrac{\text{d}v}{\text{d}x}=x \implies v=\dfrac{1}{2}x^2

Therefore:

\begin{aligned}\displaystyle \int u \dfrac{dv}{dx}\:dx & =uv-\int v\: \dfrac{du}{dx}\:dx\\\\\implies \displaystyle \int x \ln x\:\:\text{d}x & = \ln x \cdot \dfrac{1}{2}x^2-\int \dfrac{1}{2}x^2 \cdot \dfrac{1}{x}\:\:dx\\\\& = \dfrac{1}{2}x^2\ln x -\int \dfrac{1}{2}x\:\:dx\\\\& = \dfrac{1}{2}x^2\ln x - \dfrac{1}{4}x^2+\text{C}\end{aligned}

Learn more about integration here:

brainly.com/question/27805589

brainly.com/question/27983581

brainly.com/question/27759474

5 0
2 years ago
Twice the sum of eight and three times a number is seventy six. What is the number
Dahasolnce [82]

From the question we can deduce the formula to be 16 + 3n = 76

3n - 76 - 16

3n = 60

n = 20

20 is the answer.

3 0
2 years ago
Dot plots are often used for what 2 sets of data
emmainna [20.7K]

Answer:

categorical or quantitative data

Step-by-step explanation:

6 0
2 years ago
An electrician charges $45 for each home visit plus $19.95 every hour he spends working. Which sentence could be used to find C,
VARVARA [1.3K]

Answer:

C= 45 + 19.95h

Step-by-step explanation:

45 for each home vist means one time payment

19.95 ever hour means you are charged 19.95 every hour

H= hour

4 0
3 years ago
in 4 minutes Liaa can type 140 words. If she has an essay taht is 700 words long , about how long will it take Liana to type it
Zanzabum

Answer: Lol your in collage I don't believe it anyway the answer is 20 min on the dot  

6 0
2 years ago
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